Multifaceted assessment of children's inversion understanding.

The current study was aimed at examining various theoretical issues concerning children's inversion understanding (i.e., its factor structure, development, and relation with mathematics achievement) using a multifaceted assessment. A sample of 110 fourth to sixth graders was evaluated in three different measures of inversion understanding: evaluation of examples, explicit recognition, and application of procedures. The participants were also evaluated on their mathematics achievement. A one-factor structure best explains inversion understanding involving different arithmetic operations. Grade-related improvements were observed in some facets of inversion understanding. Latent profile analysis using the three inversion measures revealed seven classes of children with different inversion profiles. Furthermore, classes with better inversion understanding also had higher mathematics achievers. The current findings provide evidence to support the multifaceted nature of inversion understanding, grade-related improvements in children's inversion understanding as well as the relation between inversion understanding and mathematics achievement.